Question

fill in the blanks
given: $overrightarrow{ba}perpoverrightarrow{bc}$
prove: $angle3$ and $angle4$ are complementary.
answer attempt 1 out of 5
because $overrightarrow{ba}perpoverrightarrow{bc}$, $angle abc$ is a $mangle3$
$mangle4$
. because of the
postulate, $mangle3 + mangle4=$
$mangle abc$.
so, using the substitution property,
$+$
$=$
. then by definition, $angle3$ and $angle4$ are complementary.

Explanation:

Step1: Define angle - type

Since $\overrightarrow{BA}\perp\overrightarrow{BC}$, $\angle ABC$ is a right - angle, and $m\angle ABC = 90^{\circ}$.

Step2: Apply angle - addition postulate

By the angle - addition postulate, $m\angle3 + m\angle4=m\angle ABC$.

Step3: Use substitution

Using the substitution property, $m\angle3 + m\angle4 = 90^{\circ}$.

Answer:

Because $\overrightarrow{BA}\perp\overrightarrow{BC}$, $\angle ABC$ is a right - angle, and $m\angle ABC = 90^{\circ}$. Because of the angle - addition postulate, $m\angle3 + m\angle4=m\angle ABC$. So, using the substitution property, $m\angle3$+$m\angle4$ = $90^{\circ}$. Then by definition, $\angle3$ and $\angle4$ are complementary.